SOME REMARKS ON THE USE OF THE INVERSE HESSIAN MATRIX OF THE LIKELIHOOD FUNCTION IN THE ESTIMATION OF STATISTICAL PROPERTIES OF PARAMETERS

The computation of statistical properties in nonlinear parameter estimation is generally carried out using the hessian matrix of the likelihood function according to approximated expressions of the type V-upsilon congruent-to H-1, where V-upsilon is the estimated variance-covariance matrix of the parameters, and H is the hessian matrix of the likelihood function L at a maximum. It is shown in this paper that this approximation, based on local expansion of H, can lead to large deviations from the exact values whenever the truncation of L after the second term of the expansion is not sufficient. Furthermore, a method for continuously monitoring the validity of this approximation is proposed, and an alternative procedure is examined for the computation of V-upsilon, whenever the usual estimation based on the hessian matrix cannot be used.